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Chapter 3: Q28 (page 98)

Given: GKbisects∠JGI

m∠H=m∠1

Prove: GK∥HI

Short Answer

Expert verified

It is proved that GK∥HI.

Step by step solution

01

Step 1. Apply exterior angle theorem.

From the given diagram it can be observed that ∠JGIis exterior angle and are remote interior angles, such that,

m∠JGI=m∠H+m∠I=m∠I+m∠I=2m∠I

02

Step 2. Apply definition of angle bisector.

Here, GK¯bisects ∠JGI, therefore,

m∠KGI=12m∠JGI=12×2m∠I=m∠I

Which implies that the alternative angles are equal.

03

Step 3. Description of step.

If the two lines are intersected by a transversal and alternative angle are equal then the two lines are parallel. Therefore, .

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Most popular questions from this chapter

Classify each pair of angles as alternate interior angles, same-side interior angles, corresponding angles, or none of these.

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